Wining a small engagement wouldn't really qualify as a "pasting" though would it? A pasting would be something big like the Battle of Midway. With the Klingons as the Japanese, and Starfleet as the Americans.
Riker could have been exaggerating.
For all we know, Archer IV could have been a Federation Pyrrhic victory that crippled the fleet beyond all repair.
Aren't you doing here what you have been saying (earlier in the thread) others aught NOT do? "For all we know"; "maybe the Klingons gained some edge we weren't told about"; "maybe the UFP was in some dire straits going into the war we weren't told about"; etc. All such suppositions were responded to by yourself with the notion that none of that matters, because it's all just speculation. The direct implication from what is on screen is that the Feds were losing the war. Similarly, I think it's quite obvious that Riker's line is CLEARLY meant to indicate that Archer IV was an engagement that went heavily in Starfleet's favor. If the default position is to take Picard at his word, and not assume that he is exaggerating or lying without a reason (and I agree with you that it IS the default position), it is also the defaul position to assume that Riker was correctly recounting a recent event that went quite well for Starfleet (one that, in all likelihood, the Ent-D was present for). Of course, that one victory wouldn't upset the overall balance of the war.
All of that said... I DO agree that the clear implications of YE are that the UFP was losing that war, and rather badly. Sure, in
theory, Picard COULD have been lying, or exaggerating, or what have you. But that's all fan speculation. Which is fine; there's nothing wrong with speculation, that's partly why we're even here on this BBS, but it is just that. There is no reason to think that the creators of the show had any of these things in mind when they wrote the episode. "Yesterday's Enterprise" is about an alternate reality in which the UFP was fighting, and badly losing, a long war against the Klingons.
All of THAT said... I don't like it.

I don't deny that YE is about what it is about, but I feel it contradicts the rest of the filmed canon. If you were to remove YE, I think the evidence favors a Federation victory, so my problem with YE is that it contradicts everything else. I think there could be specific reasons for why the war went so badly for the Feds, and that's an interesting topic to ponder, but it would still be just speculation (and again, nothing wrong with that, it's fun.)